Hankel transforms of general monotone functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909095373570048 |
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| author | Debernardi, Alberto |
| author_facet | Debernardi, Alberto |
| contents | We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel-Olivier test for real-valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hankel transforms of general monotone functions Debernardi, Alberto Classical Analysis and ODEs 42A38 We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel-Olivier test for real-valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series. |
| title | Hankel transforms of general monotone functions |
| topic | Classical Analysis and ODEs 42A38 |
| url | https://arxiv.org/abs/2402.03974 |